Actuation cell response and mapping determinations for web forming machines

ABSTRACT

A standard control signal for a web forming machine is temporarily interrupted and replaced by a perturbing signal or signgals which are applied to one, a grouping, or all of a series of actuation cells of the web forming machine. One or more actuation cells are driven with an alternating perturbing signal(s) which generate a corresponding action in the actuation cell(s). The perturbing signal(s) alternates from a neutral position of the cell and is selected to minimize means effects over any given period of time. The effects of the alternating signal(s) on the web appear within the area of the web which is affected by the actuation cell(s) such that the mapping and the response of the actuation cell(s) can be determined by monitoring that poriton of the web which is formed while the alternating signal(s) is applied to the actuation cell(s). The mapping(s) and/or response(s) of the actuation cell(s) are obtained by correlating the perturbing signal(s) and a web property signal or profile signal obtained by monitoring the web formed by the machine. The perturbing signal(s) is defined by a pseudo-random binary sequence with multiple signals being selected to be statistically independent of one another. To ensure that the web is not perturbed beyond defined specifications, the perturbing signal preferably is gradually increased in amplitude and is terminated individually for each actuation cell upon reaching a usable amplitude.

BACKGROUND OF THE INVENTION

The present invention relates generally to machines for forming webs ofsheet material and, more particularly, to a method and apparatus fordetermining cross direction responses and mappings of actuation cellsused to control the operation of such machines.

Machines which produce webs of sheet material such as paper, plastic andaluminum, face common process control problems in producing webs whichsatisfy specifications for the given sheet material. Web specificationscommonly include ranges for characteristics of the web includingthickness, moisture content, weight per unit area and the like. Qualitycontrol is complicated since the specified characteristics vary in boththe machine direction (MD) or direction of movement of the web throughthe machine and in the machine cross direction (CD) or laterally acrossthe web.

The MD variations are generally affected by factors that impact theentire width of the web, such as machine speed, the source of basematerial being formed into a web by the machine, common supplies ofworking fluids like steam, and similar factors. CD variations,represented by profiles or profile signals, are normally controlled byarrays of actuation cells distributed across the width of the machine.On paper making machines, for which the present invention isparticularly applicable, the CD actuation cells include basis weightactuators which control the slice of a headbox, steam shower nozzles,infrared (IR) heaters which control CD moisture variations, and otherknown devices.

Adjustment of CD actuation cells generally affects a portion of theprofile that is wider than the individual actuation cells. Thus, forcontrolling the CD profile of a web forming machine, it is important toknow which portion of the profile is affected by each CD actuation celland how the profile is changed by adjustments of each CD actuation cell.The functional relationship that describes which part of the profile isaffected by each CD actuation cell is called "mapping" of the CDactuator cells. The functional curve that indicates how the processprofile is changed by the adjustment of a CD actuation cell is calledthe "response" of the CD actuation cell.

Not only does the CD response of an actuator cell typically spread overa much wider area than the area of the cell itself, but also the CDmapping of an actuator cell can vary or shift for different operatingconditions. To obtain a desired profile for the web of sheet materialbeing formed, it is essential to have response and mapping informationwhich precisely corresponds to each actuation cell and also to thedifferent operating conditions which the cell may encounter.

In the past, response information typically has been determined on-lineby means of feedback arrangements. In these systems, the control signalswhich are passed to the machine to maintain the web forming processwithin suitable limits are monitored and compared to a profile signalwhich is generated by monitoring the web of material within the machineor as it emerges from the machine. Unfortunately, since the controlsignals must be substantially limited in terms of amplitude excursions,the resulting response and mapping characteristics are not asrepresentative as is desired for accurate control of the machine.

Another system has been described for determining both response andmapping information by interrupting a system controller and thenchanging the setting of a given actuation cell. The actuation cell ischanged a number of times and the resulting changes in the web aremonitored. By summing and otherwise processing these changes, theresponse and mapping for the actuation cell can be determined.Unfortunately, the described system requires a substantial period oftime to evaluate one or more series of actuation cells. Further, thereis no assurance that the web being produced during the evaluation willbe within required specification limits such that the web can be used.

Accordingly, there is a need for improved determination of the responseand mapping characteristics of the individual actuation cells of webforming machines. The response and mapping characteristics should bequickly and accurately obtained, even while the machine is operating andwithout adversely affecting the quality of the web of material beingformed. Preferably, any method and/or apparatus for determining theresponse and mapping characteristics could be inexpensively incorporatedinto new machines and also retrofitted into existing machines withsubstantially equal improvements in the operations of the existingmachines.

SUMMARY OF THE INVENTION

This need is met by the method and apparatus of the present inventionwherein a standard control signal for a web forming machine istemporarily interrupted and replaced by a perturbing signal which isapplied to one, a grouping, or all of a series of actuation cells of theweb forming machine. In its most basic implementation, an actuation cellis driven with an alternating perturbing signal which generates acorresponding action in the actuation cell. The signal alternates from aneutral position of the cell and is selected to minimize mean effectsover any given period of time. The effects of the alternating signal onthe web appear within that area of the web which is affected by theactuation cell such that the mapping and the response of the actuationcell can be determined by monitoring that portion of the web which isformed while the alternating signal is applied to the actuation cell. Inthe present invention, the mapping and/or response of the actuation cellare obtained by correlating the perturbing signal and a web propertysignal or profile signal obtained by monitoring the web formed by themachine.

To speed up the determination of the mapping and response of all theactuation cells of a web forming machine, perturbing signals can beapplied to groups of actuation cells, with cells within each group beingspaced from one another by a sufficient distance to substantiallyprevent interference between or among perturbing signals. The resultingmappings and responses can be interpolated or additional groups can bestimulated to arrive at mappings and responses for all the actuationcells.

To further speed up the determination, all of the actuation cells can bedriven simultaneously with the resulting web effects being monitored andseparated to determine the mappings and responses of all of theactuation cells. For simultaneous excitation of all actuation cells,each cell is driven with a particular sequence of alternating signalswhich is unique for that cell and hence can be recognized in theresulting perturbations of the portion of the web which is formed whilethe signals are being applied. Recognition of the perturbations due toindividual actuation cells is possible even though the perturbations ofadjacent cells overlap one another and visually appear inseparable,since the activation signals are selected to be substantiallyindependent of one another.

To this end, activation signals are preferably defined by pseudo-randombinary sequences which are selected to be statistically independent ofone another. To simplify selection of independent sequences, it has beenrecognized that a pool of independent sequences may be repeated ingroupings across the machine, provided the groupings are of sufficientsize that each signal in one group is separated from the same signal inan adjacent group such that there is substantially no interferencebetween the two. To ensure that the web is not perturbed beyond definedspecifications for the web, the perturbing signal preferably isgradually increased in amplitude. The perturbing signal amplitude isincreased until its result is sufficiently recognizable in the web tosatisfactorily determine the mappings and responses of the actuationcells of the web forming machine but not to the point of exceedingspecification limits.

In accordance with one aspect of the present invention, a method fordetermining the cross direction responses and mappings of actuationcells extending across the width of a machine used for manufacturing aweb of sheet material comprises the steps of: applying a perturbingsignal to at least one actuation cell, the perturbing signal alternatingabout a neutral state of the actuation cell to minimize mean effectsover any given time period of signal application; measuring a propertyof the web of sheet material produced by the machine during applicationof the perturbing signal to generate a corresponding web propertysignal; and, correlating the perturbing signal and the web propertysignal to determine the cross direction response and mapping of the atleast one actuation cell for the property.

In accordance with another aspect of the present invention, a method fordetermining the cross direction responses and mappings of actuationcells extending across the width of a machine used for manufacturing aweb of sheet material comprises the steps of: applying perturbingsignals to a plurality of the actuation cells, the perturbing signalsalternating about a neutral state of the actuation cells to minimizemean effects over any given time period of signal application; measuringa property of the web of sheet material produced by the machine duringapplication of the perturbing signals to generate a corresponding webproperty signal; and, correlating the perturbing signals and the webproperty signal to determine the cross direction responses and mappingsof the plurality of actuation cells for the property.

The method may further comprise the step of modulating the perturbingsignal such that its amplitude is gradually increased from a low levelto a level at which web property perturbations resulting from theperturbing signal are distinguishable from noise perturbationsencountered during normal machine operation, but web specifications arenot compromised. The durations of alternations of each perturbing signalpreferably are randomly distributed between defined limits to ensuredetection of resulting perturbations. The step of applying a perturbingsignal may comprise applying a perturbing signal to a plurality ofactuation cells which are spaced apart from one another by a distancesuch that perturbations generated by the application of the perturbingsignal to any one of the plurality of actuation cells does notsubstantially affect perturbations generated by the application of theperturbing signal to any other one of the plurality of actuation cells.

To fully define the response of the actuation cells, the method furthercomprises the step of determining the center of the response for theactuation cells. To substantially prevent interference between closelypositioned actuation cells, the perturbing signals may comprise aplurality of substantially independent excitation patterns. Preferably,the perturbing signals comprise a plurality of statistically independentpseudo-random binary sequences, particularly where perturbing signalsare applied to all of the actuation cells. To reduce the number of suchsequences which are required for a given machine, the perturbing signalscan be applied in groups of repetitively occurring statisticallyindependent pseudo-random binary sequences, the groups being ofsufficient size such that recurring perturbing signals are spaced fromone another by a sufficient distance to preclude significantinterference therebetween.

In accordance with yet another aspect of the present invention, a methodfor determining the cross direction responses and mappings of actuationcells extending across the width of a machine used for manufacturing aweb of sheet material comprises the steps of: applying a perturbingsignal u(k,t) to a k-th actuation cell during time t, the perturbingsignal u(k,t) alternating about a neutral state of the k-th actuationcell to minimize mean effects over any given time period of signalapplication; measuring a property of the web of sheet material producedby the machine during application of the perturbing signal u(k,t) togenerate a corresponding web property signal y(i,t) where i indicatesthe cross direction location and t indicates the time of application;and, correlating the perturbing signal u(k,t) and the web propertysignal y(i,t) to determine the cross direction response r(k,i) of thek-th actuation cell at the i-th cross direction location which alsodefines the mapping of the k-th actuation cell into the cross directionlocations i for the property. The step of correlating the perturbingsignal u(k,t) and the web property signal y(i,t) preferably comprisesthe steps of taking the covariance of u(k,t) and y(i,t+d) and dividingthe resulting covariance with the covariance of u(k,t) with itself,where d is the transportation delay between applying the perturbingsignal u(k,t) and measuring the web of sheet material to generate theweb property signal y(i,t) plus dynamic delays associated with controlof the k-th actuator cell.

In accordance with still another aspect of the present invention, asystem for determining the cross direction responses and mappings ofactuation cells extending across the width of a machine used formanufacturing a web of sheet material comprises excitation patterngenerating means for applying a perturbing signal to at least oneactuation cell. The perturbing signal alternates about a neutral stateof the actuation cell to minimize mean effects over any given timeperiod of signal application. Sensor means monitor the web of sheetmaterial and generating a profile signal representative of one or morecharacteristics of the web of sheet material in the machine crossdirection. To determine the cross direction response and mapping of theat least one actuation cell for one or more characteristics, processormeans are provided for correlating the perturbing signal and the profilesignal. The amplitude of the perturbing signal is gradually increasedfrom a low level to a level at which web characteristic perturbationsresulting from the perturbing signal are distinguishable from noiseperturbations encountered during normal machine operation. In this way,the system can be assured of accurately determining mappings andresponses without forcing the web outside specified limits.

In accordance with an additional aspect of the present invention, asystem for determining the cross direction responses and mappings ofactuation cells extending across the width of a machine used formanufacturing a web of sheet material comprises excitation patterngenerating means for applying perturbing signals to a plurality of theactuation cells. The perturbing signals alternate about neutral statesof the actuation cells to minimize mean effects over any given timeperiod of signal application. Sensor means monitor the web of sheetmaterial and generate a profile signal representative of one or morecharacteristics of the web of sheet material in the machine crossdirection. To determine the cross direction response and mapping of theplurality of actuation cells for one or more characteristics, processormeans are provided for correlating the perturbing signals and theprofile signal.

In accordance with yet an additional aspect of the present invention, asystem for determining the cross direction responses and mappings ofactuation cells extending across the width of a machine used formanufacturing a web of sheet material comprises excitation patterngenerating means for applying a perturbing signal u(k,t) to a k-thactuation cell during time t. The perturbing signal u(k,t) is alternatedabout a neutral state of the k-th actuation cell to minimize meaneffects over any given time period of signal application. Sensor meansmonitors the web of sheet material and generates a profile signal y(i,t)where i indicates the cross direction location and t indicates the time,the profile signal being representative of one or more characteristicsof the web of sheet material in the machine cross direction andincluding the effects of the perturbing signal u(k,t) on the one or morecharacteristics. Processor means are provided for correlating theperturbing signal u(k,t) and the profile signal y(i,t) to determine thecross direction response r(k,i) of the k-th actuation cell at the i-thcross direction location which also defines the mapping of the k-thactuation cell into the cross direction locations i for the one or morecharacteristics.

It is thus an object of the present invention to provide an improvedmethod and apparatus for more rapidly and accurately determining themappings and responses of actuation cells of web forming machines; toprovide an improved method and apparatus for more rapidly and accuratelydetermining the mappings and responses of actuation cells of web formingmachines by applying perturbing signals to the actuation cells,measuring the resulting perturbation signals in the web, and correlatingthe perturbing signals with the perturbation signals; to provide animproved method and apparatus for more rapidly and accuratelydetermining the mappings and responses of actuation cells of web formingmachines wherein perturbing signals which alternate from a neutralposition are applied to the actuation cells and are formed to minimizemean effects to the web over any given period of time such that themappings and responses of actuation cells can be determined withoutinterrupting or interfering with operation of the machine; and, toprovide an improved method and apparatus for more rapidly and accuratelydetermining the mappings and responses of actuation cells of web formingmachines wherein perturbing signals comprising a pool of pseudo-randombinary sequences are applied to the actuation cells and are correlatedwith resulting perturbation signals to arrive at the mappings andresponses of the actuation cells.

Other objects and advantages of the invention will be apparent from thefollowing description, the accompanying drawings and the appendedclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic perspective plan view of a paper making machinefor which the present invention is particularly applicable illustratinga headbox, a steam profiler and a web sensor platform, respectively, andalso various web conveying rollers and wires;

FIG. 2 is a block diagram of a prior art arrangement for identifying themappings and responses of cell actuators from process control signalsand a web profile signal;

FIG. 3 is a block diagram of an arrangement for determining actuationcell mappings and responses of a web forming machine in accordance withthe present invention;

FIG. 4 is a graph of an excitation pattern usable in the presentinvention;

FIG. 5 is a graph of a response pattern which would result in theprofile or web property signal as the result of the excitation patternshown in FIG. 4;

FIG. 6 shows a perturbing signal corresponding to the excitation patternof FIG. 4 which is applied to the 20th actuation cell of a web formingmachine;

FIG. 7 shows the responses to the perturbing signal of FIG. 6;

FIG. 8 shows both a filtered and unfiltered response curve for the 20thactuator cell resulting from a correlation of the perturbing signal andthe responses to the perturbing signal of FIGS. 6 and 7, respectively;

FIG. 9 shows two substantially independent excitation signals which areapplied to the 20th and 22nd actuation cells of a web forming machine;

FIG. 10 shows the overlapping perturbations which result in the profileor web property signals in response to the excitation signals of FIG. 9;

FIG. 11 shows the individual response curves for the 20th and 22ndactuator cells, respectively, which are calculated in accordance withthe present invention when in response to the signals of FIGS. 9 and 10;and

FIG. 12 shows a solid-line response curve calculated in accordance withthe present invention from individual excitation of the 20th cell withthe signal of FIG. 6 and a dotted-line response curve calculated underthe multiple excitations of the 20th cell and the 22nd cell with thesignals of FIG. 9.

DETAILED DESCRIPTION OF THE INVENTION

While the present invention is generally applicable to machines formaking or processing webs of sheet material, it is particularlyapplicable to paper making machines and accordingly will be describedherein with reference to such a machine. FIG. 1 is a schematicperspective plan view of a paper making machine 100 including a headbox102 which defines a headbox slice 104 by a slice lip 106 which iscontrolled along its length by actuator cells comprising basis weightactuators 108. Pulp slurry is conveyed to the headbox 102 via a stockpipe 110 such that slurry can be applied to a wire 112 to form a paperweb 114. As the web 114 passes along the wire 112 and other parts of thepaper making machine 100, it is processed by passing over foils,deflectors and suction boxes (not shown).

The web 114 may also be acted upon by one or more processing stationsalong the length of the machine 100, for example by a steam profiler 116which includes cell actuators such as steam shower nozzles. While thepresent invention will be described with reference to control of thebasis weight actuators 108, it is noted that it is generally applicableto the control of any form of actuator cell including steam showernozzles, water spray IR heaters, caliper profilers and other cellactuators whether currently used or developed in the future to control aweb profile of sheet material. The web 114 also passes through sensormeans comprising a machine cross direction (CD) web measurement platform118 and a sensor 120 such as a nucleonic or other appropriate sensorsupported by and moved along the platform 118. The sensor 120 generatesa profile signal representative of one or more characteristics of theweb in the machine CD to permit control of the characteristics byprocessor means incorporated into an operator station 121 to therebyimprove the quality of the web 114.

While a scanning sensor 120 is illustrated in FIG. 1, the presentinvention is equally applicable and, in fact, more advantageous if usedwith a sensor which simultaneously monitors the entire CD of the web114. For example, operation of the present invention to determine themapping and response of an entire series of actuation cells may beperformed in as little as 15 minutes or possibly less where an array ofCD monitors performs simultaneous monitoring.

In the past, response information has been determined on-line by meansof feedback arrangements illustrated by the block diagram of FIG. 2. Inthese systems, process control signals are generated by a controller 122in response to the web profile signal generated by the sensor 120 and atarget signal which defines the specification limits for the web 114.The process control signals are passed to actuation cells, such as thebasis weight actuators 108, of a process to be controlled represented bythe process block 124. The controller 122 utilizes parameters generatedby an on-line response identifier 126 in response to the process controlsignals from the controller 122 and the profile signal from the sensor120.

The response identifier 126 can be operated in a known manner, forexample as described in a paper entitled "Adaptive Profile Control forSheetmaking Processes" by S.-C. Chen, R. M. Snyder and R. G. Wilhelm,Jr. which was presented at the 6th International IFAC/IFIP/IMEKOConference on Instrumentation and Automation in the Paper, Rubber,Plastics and Polymerization Industries (PRP-6), held on Oct. 27-29, 1986in Akron, Ohio, which paper is incorporated herein by reference.Unfortunately, since the process control signals must be substantiallylimited in terms of amplitude excursions, the resulting response andmapping characteristics are not as representative as is desired foroptimum control of the machine 100.

An off-line system has also been described by A. Graser and W.Neddermeyer in a paper entitled "Self-Tuning Cross Profile Control For APaper Making Machine", IFAC Application in Process Control, Istanbul,Turkey, 1986. However, operation of this system is time consuming anddoes not assure that the web being formed or processed is maintainedwithin specification limits such that the web can be used.

Mappings and responses of actuation cells, such as the basis weightactuators 108, are relatively quickly and accurately obtained by themethod and apparatus of the present invention. In the present invention,the process control signals from the controller 122 of the machine 100are temporarily interrupted and replaced by an alternating perturbingsignal generated by a pattern generator 128. The perturbing signal isapplied to one, a grouping, or all of a given variety of actuation cellsof the machine 100 such as the actuators 108, see FIG. 3. The effects ofthe alternating signal on the web appear within that area of the webwhich is affected by the actuation cell(s) such that the mapping and theresponse of the actuation cell(s) can be determined by monitoring thatportion of the web which is formed while the alternating signal isapplied to the actuation cell(s).

In the present invention, the mapping and/or response of each actuationcell is obtained by correlating or matching the patterns of theperturbing signal and a web property signal or profile signal obtainedby monitoring the web formed by the machine 100 via the sensor 120. Inthe block diagram of FIG. 3, the correlation is performed by a patternrecognition identifier 130. It is noted that more than one variety ofactuation cells can be probed simultaneously with the present inventionprovided the characteristics of the web affected by the differingactuation cells can be simultaneously monitored and do not interact withone another. Interaction of differing cell varieties could even betolerated provided that independent signals were applied and suchinteraction did not cause the web characteristics to exceedspecification limits.

A key element of the present invention is the excitation pattern orpatterns which are generated by the pattern generator 128. In practice,correlation operations and the generation of excitation signal patternsis performed by processor means which may, for example, be incorporatedinto the operator station 121 of FIG. 1. It is noted that any perturbingsignal applied to an actuation cell for process probing or excitationpurposes should be of sufficient magnitude to generate a perturbationwhich can be distinguished from noise perturbations generated by normaloperation of the process. However, the perturbing signal preferably isalso sufficiently small that the web 114 remains within thespecification limits, since otherwise the machine production duringprobing operations is not usable.

With this in mind, the excitation pattern should have the followingproperties: 1) the perturbing signal should alternate from a neutralposition of the actuating cell being perturbed; 2) the perturbing signalshould be selected to minimize mean effects to the characteristics ofthe web being probed over any given period of time; 3) at least forinitial probing of a process, the amplitude of the perturbing signalshould be gradually increased from a very low level if not zero until anidentifiable, usable perturbation is observable in the web, an allowablemechanical limit of the actuation cell is reached, or a specified timelimit for application of the perturbing signal has been exceeded; and,4) the time duration of each movement is randomly distributed betweenspecified limits dependent upon the actuation cell being probed, e.g.longer time durations are required for a web which is being scanned, forexample 2 to 10 scans, as opposed to one which is being monitoredsimultaneously across its entire width.

An excitation pattern 132 which meets these criteria is shown in FIG. 4and a corresponding response pattern 134 which would result in theprofile or web property signal as the result of the excitation pattern132 is shown in FIG. 5. The pattern alternates in the form of apseudo-random binary sequence from the neutral position of the actuationcell which is determined at the time the excitation pattern signal is tobe applied. The mean effects on the web 114 over any given period oftime is limited by the alternations about the neutral position and theduration limits on each alternation. The amplitude of the alternations,starting from substantially zero, is increased until the response issufficiently large to be distinguished from the process noise (or themechanical or time limits are reached).

It is noted that the response pattern shown in FIG. 5 has beenexaggerated for descriptive purposes since the perturbations are to belimited to levels within the specifications limits to prevent productionof unusable product. Such large excitations are not required foroperation of the method and apparatus of the present invention. Further,while patterns having all of the noted desired properties are preferred,several other patterns can be used if desired in given applications ofthe invention. For example, square waves, sine waves and regularpseudo-random binary sequences can be used in certain applications. Suchalternate patterns are particularly applicable where individualactuation cells or groups of separated actuation cells are to be probed.

When a perturbing signal 136 corresponding to the excitation pattern 132shown in FIG. 4 is applied to an actuation cell, for example the 20thcell as shown in FIG. 6, the responses to the perturbing signal 136appear within a certain area 138 of the web 114 and are recognized bythe sensor 120 as shown in FIG. 7. In the area 138 of FIG. 7 where theresponses can be seen, the pattern of the responses are similar to theperturbing signal 136 or excitation pattern 132. The correlation betweenthe perturbing signal 136 and the resulting profile signals shown inFIG. 7 produces the response and mapping of the probed or excitedactuation cell, i.e. the 20th cell as shown in FIG. 6. The correlationor pattern matching technique is a key feature of the present invention.

FIG. 7 illustrates the web measurements at all CD locations while theperturbing signal 136 is applied to the 20th actuation cell. The visibleresponses to the perturbing signal disappear beyond a certain CDdistance from the center location of the primary response. The CD rangethat is affected by the perturbing signal 136 represents the mapping ofthe probed or excited actuation cell. The correlation between theperturbing signal 136 or excitation pattern 132 and the visibleresponses within the area 138 determines the size of the response ateach CD location and the mapping of the probed or excited actuationcell. Appropriate correlation calculations for use in the presentinvention will now be described.

We will define u(k,t) as representing the perturbing signal 136 appliedto the k-th actuation cell during the time t. The two dimensionalmeasurements of the characteristics of the web 114 performed by thesensor 120 is represented by y(i,t) where i indicates the CD locationand t is the "time stamp" of the measurement y(i,t) and indirectlyindicates the MD location of the measurement along the web 114. Thecorrelation between u(k,t) and y(i,t) for all CD locations i iscalculated using the formula:

    r(k,i)=[covariance or likelihood function of u(k,t) and y(i,t+d)]/a(k) (1)

where

d is the transportation delay or lag between the actuation cell and themeasurement plus the dynamic delays of the actuator cell and process;

a(k) is the covariance of u(k,t) with itself; and

r(k,i) is the response of the k-th actuation cell at the i-th CDlocation.

Formula (1) can be calculated either in batches or recursively.Recursive calculation with an adjustable forgetting factor appears to bepreferable at the present time. After r(k,i) is calculated for all i, azero-phase shifting spatial filter is applied to remove the noise in theresponse curves r(k,i). The spatial filter is defined by the followingequation: ##EQU1## where [f₀, f₁, f₂, . . . , f_(s) ] are thecoefficients of a spatial filter, for example as described in thereferenced paper by Chen et al.

For the example shown in FIGS. 6 and 7, a typical response curve 140calculated from the correlation between u(k,t) and y(i,t) for all CDlocations, i, is plotted in dotted lines in FIG. 8. A filtered responsecurve 142 is also plotted in solid lines in FIG. 8. The region which isaffected by the k-th actuation cell is determined by comparing theresponse with the noise deadband for the process. The range from c_(m)to c_(n) on FIG. 8 indicates the response width of the k-th actuationcell and the scaled correlation curve between c_(m) and c_(n) is theresponse of the k-th actuation cell. The center location of the responseof the k-th actuation cell, m(k), is also preferably determined and suchdetermination can be made by applying the following formula:

    m(k)=[sum.sub.1 /sum.sub.2 ]-0.5

where

sum₁ is the sum of rf(k,i)*i for all i=c_(m) to c_(n) ; and

sum₂ is the sum of rf(k,i) for all i=c_(m) to c_(n).

A perturbing signal may be applied to a group of actuation cells acrossthe machine which cells are spaced from one another such that there issubstantially no interference between the perturbing signals. Suchsignals can be correlated with the resulting perturbations to determinethe mappings and responses of the actuation cells which were excited orperturbed. Once the responses are determined for that group of cells, adifferent group of cells can be excited to determine their responses andmappings. Alternately, a piece-wise linear interpolation can be appliedto estimate the response locations and response shapes for thoseactuation cells which have not been probed.

One of the important features of the present invention is the ability toapply multiple excitation patterns to some or all of the actuationcells, even to cells which are immediately adjacent to one another. Forsuch multiple excitation, a pool of substantially independent excitationor perturbing patterns are created and saved. Within a continuous groupof actuation cells, each pattern is unique such that it uniquelyidentifies the actuation cell to which it is applied. Thus, for anygiven continuous group of actuation cells, the unique pattern for eachcell can be thought of as a "bar code" or "cellprint" for the cell. Inthis way, the perturbations which result from exciting a given cellwithin a group of continuous cells can be identified and separated fromthe perturbations resulting from excitation of other cells within thegroup.

While the group of cells does not have to be continuous for the use of apool of substantially independent excitation or perturbing patterns, inits broadest application, the use of such a pool of patterns permits allactuation cells across a machine to be excited or probed simultaneously.Simultaneous stimulation substantially reduces the time required togenerate mappings and responses for the actuation cells. Forsimultaneous stimulation, the actuation cells are divided into aplurality of groups of cells. The pool of excitation signals is orderedsuch that the patterns are applied to the groups in the same order,i.e., pattern #1, pattern #2, .... pattern #x; pattern #1, pattern #2,.... pattern #x; pattern #1, pattern #2, .... pattern #x; and so forth,until each actuation cell is assigned a unique pattern within its group.In this way, repeated patterns are spaced from one another by asufficient distance that there is substantially no interference betweenor among repeated patterns.

Preferably, the pool of patterns are selected from a large number ofpsuedo-random binary sequences which are generated in a known manner. Abinary sequence is selected to be within the pool if the sequence has acorrelation with all other sequences within the pool which is less than5%. Accordingly, all sequences within the pool are statisticallyindependent of one another.

When any group of actuation cells is excited or probed by acorresponding group of different patterns from the pool of substantiallyindependent patterns, each cell is actuated with its own identifyingexcitation pattern. For example, two such signals 144, 146 are shown asbeing applied to two cells, the 20th and 22nd cells, in FIG. 9. Theoverlapping perturbations resulting in the area 148 of the profile orweb property signals generated by the sensor 120 are shown in FIG. 10.

Although it is not easy to visualize the separate impacts of the signals144, 146 on the resulting perturbations in the area 148, the responsecurves for the 20th and 22nd actuation cells can be accuratelyidentified and distinguished by applying the correlation calculationspreviously defined. FIG. 11 shows the individual response curves 150,152 for the 20th and 22nd actuators, respectively, which are calculatedwhen the correlation calculations of the present application are appliedto the signals of FIGS. 9 and 10.

To compare the accuracy of response curves which are generated from theapplication of individual excitation signals to the response curveswhich are generated by the application of multiple excitation signals,the 20th actuation cell of a machine was excited with the signal 144alone and together with the excitation of the 22nd cell with the signal146. FIG. 12 shows the solid-line response curve 154 calculated inaccordance with the present invention from individual excitation of the20th cell with the signal 144 and the dotted-line response curve 156calculated with the multiple excitations of the 20th cell with thesignal 144 and the 22nd cell with the signal 146. As is apparent, theresponse curves 154 and 156 are almost identical to one another.

Accordingly, it is possible with the present invention to probe allactuation cells simultaneously to obtain complete mapping and responseinformation at one time. However, it may be preferred to probe theactuation cells of a machine sequentially in several groups. In eachgroup, a set of substantially independent patterns is applied to theactuation cells. The probing operation is performed group by group untilall actuation cells are probed and a complete set of response andmapping information is generated. Of course, it is also possible toprobe a single actuation cell or a number of cells if a problem arisesin the area serviced by the cell or number of cells, which problem isidentified by variations from the web specifications.

In actual applications of the present invention, it may not be apparentwhat amplitude of excitation signal is sufficiently large to obtainusable perturbations in the web characteristics yet not so large thatthe perturbations to the web exceed acceptable specification limits. Forthese instances, a conservative approach is to start the perturbingsignal at a very small amplitude, if not zero, and to gradually increasethe amplitude of the perturbing signal as shown in FIG. 1. The amplitudeof the perturbing signal is then gradually increased until the resultingperturbations in the web reach a desired signal-to-noise ratio, amaximum mechanical limit is reached for the actuation cell or cellsbeing probed, or a time out is signaled of the probing operation.

The final amplitude is then recorded and can be used as the perturbingsignal amplitude when the actuation cell or cells are to be once againprobed under similar operating conditions. By storing a satisfactoryamplitude for the perturbing signal, the required probing time isminimized and yet the possibilities of disruption of the product beingproduced by the machine are minimized. This initialization procedure canbe utilized for any number of different sets of operating conditions,different product grades or other variables in a web forming orprocessing machine to more precisely determine initial settings forapplication of the present invention. By using the present invention foreach product grade or distinct operating condition for a machine anddeveloping data bases corresponding to the grades/conditions, shortertransition times are possible for grade change and machine start-up.

The present invention can be used as either a start-up procedure when anew machine is installed or as an on-line identification and correctionprocedure for an existing machine. When a process is running with anautomatic controller for CD actuation cells, the invention can betriggered by a controlled variable, such as sheet thickness, exceedinglimits defined by the specifications for the product being produced. Allactuation cells can be evaluated by the present invention or only thosecells which correspond to the portion of the web which has exceeded thelimits. In any event, all or a portion of the automatic control issuspended temporarily while the probing operation is performed on all orthat portion of the actuation cells which have caused the problem. Afterthe response curves and mapping information have been determined, theautomatic control is resumed with the updated response and mappinginformation.

As previously noted, the probing signal may be gradually increased untila functional amplitude is attained. It is important that the perturbingsignal be stopped after satisfactory results have been obtained toprevent any further disturbance in the product being produced by themachine. The determination to stop a perturbing signal preferably shouldbe made individually for each actuation cell.

Having thus described the method and apparatus for determining theresponse and mapping of actuation cells of web forming or processingmachines of the present invention in detail and by reference topreferred embodiments thereof, it will be apparent that modificationsand variations are possible without departing from the scope of theinvention defined in the appended claims.

What is claimed is:
 1. A method for determining the cross directionresponses and mappings of actuation cells extending across the width ofa machine used for manufacturing a web of sheet material, the methodcomprising the steps of:applying a perturbing signal to at least oneactuation cell, said perturbing signal alternating about a neutral stateof said actuation cell to minimize mean effects over any given timeperiod of signal application; measuring a property of the web of sheetmaterial produced by the machine during application of said perturbingsignal to generate a corresponding web property signal; and correlatingthe perturbing signal and the web property signal to determine the crossdirection response and mapping of said at least one actuation cell forthe property.
 2. A method for determining the cross direction responsesand mappings of actuation cells extending across the width of a machineused for manufacturing a web of sheet material as claimed in claim 1further comprising the step of modulating said perturbing signal suchthat its amplitude is gradually increased from a low level to a level atwhich web property perturbations resulting from said perturbing signalare distinguishable from noise perturbations encountered during normalmachine operation.
 3. A method for determining the cross directionresponses and mappings of actuation cells extending across the width ofa machine used for manufacturing a web of sheet material as claimed inclaim 2 wherein the duration of alternations of said perturbing signalis randomly distributed between defined limits.
 4. A method fordetermining the cross direction responses and mappings of actuationcells extending across the width of a machine used for manufacturing aweb of sheet material as claimed in claim 1 wherein the step of applyinga perturbing signal comprises applying a perturbing signal to aplurality of actuation cells which are spaced apart from one another bya distance such that perturbations generated by the application of saidperturbing signal to any one of said plurality of actuation cells doesnot substantially affect perturbations generated by the application ofsaid perturbing signal to any other one of said plurality of actuationcells.
 5. A method for determining the cross direction responses andmappings of actuation cells extending across the width of a machine usedfor manufacturing a web of sheet material as claimed in claim 1 furthercomprising the step of determining the center of the response of said atleast one actuation cell.
 6. A method for determining the crossdirection responses and mappings of actuation cells extending across thewidth of a machine used for manufacturing a web of sheet material, themethod comprising the steps of:applying perturbing signals to aplurality of said actuation cells, said perturbing signals alternatingabout a neutral state of said actuation cells to minimize mean effectsover any given time period of signal application; measuring a propertyof the web of sheet material produced by the machine during applicationof said perturbing signals to generate a corresponding web propertysignal; and correlating said perturbing signals and the web propertysignal to determine the cross direction responses and mappings of saidplurality of actuation cells for the property.
 7. A method fordetermining the cross direction responses and mappings of actuationcells extending across the width of a machine used for manufacturing aweb of sheet material as claimed in claim 6 wherein said perturbingsignals comprise a plurality of substantially independent excitationpatterns.
 8. A method for determining the cross direction responses andmappings of actuation cells extending across the width of a machine usedfor manufacturing a web of sheet material as claimed in claim 6 whereinsaid perturbing signals comprise a plurality of statisticallyindependent pseudo-random binary sequences.
 9. A method for determiningthe cross direction responses and mappings of actuation cells extendingacross the width of a machine used for manufacturing a web of sheetmaterial as claimed in claim 6 wherein perturbing signals are applied toall of said actuation cells, said perturbing signals comprising aplurality of statistically independent pseudo-random binary sequences.10. A method for determining the cross direction responses and mappingsof actuation cells extending across the width of a machine used formanufacturing a web of sheet material as claimed in claim 9 wherein saidperturbing signals are applied in groups of repetitively occurringstatistically independent pseudo-random binary sequences, said groupsbeing of sufficient size such that recurring perturbing signals arespaced from one another by a sufficient distance to preclude significantinterference therebetween.
 11. A method for determining the crossdirection responses and mappings of actuation cells extending across thewidth of a machine used for manufacturing a web of sheet material, themethod comprising the steps of:applying a perturbing signal u(k,t) to ak-th actuation cell during time t, said perturbing signal u(k,t)alternating about a neutral state of said k-th actuation cell tominimize mean effects over any given time period of signal application;measuring a property of the web of sheet material produced by themachine during application of said perturbing signal u(k,t) to generatea corresponding web property signal y(i,t) where i indicates the crossdirection location and t indicates the time of application; andcorrelating said perturbing signal u(k,t) and the web property signaly(i,t) to determine the cross direction response r(k,i) of the k-thactuation cell at the i-th cross direction location which also definesthe mapping of the k-th actuation cell into the cross directionlocations i for the property.
 12. A method for determining the crossdirection responses and mappings of actuation cells extending across thewidth of a machine used for manufacturing a web of sheet material asclaimed in claim 11 wherein the step of correlating said perturbingsignal u(k,t) and the web property signal y(i,t) comprises the steps oftaking the covariance of u(k,t) and y(i,t+d) and dividing the resultingcovariance with the covariance of u(k,t) with itself, where d is thetransportation delay between applying the perturbing signal u(k,t) andmeasuring the web of sheet material to generate the web property signaly(i,t) plus dynamic delays associated with control of said k-th actuatorcell.
 13. A system for determining the cross direction responses andmappings of actuation cells extending across the width of a machine usedfor manufacturing a web of sheet material, the systemcomprising:excitation pattern generating means for applying a perturbingsignal to at least one actuation cell, said perturbing signalalternating about a neutral state of said actuation cell to minimizemean effects over any given time period of signal application; sensormeans for monitoring the web of sheet material and generating a profilesignal representative of one or more characteristics of the web of sheetmaterial in the machine cross direction; and processor means forcorrelating the perturbing signal and the profile signal to determinethe cross direction response and mapping of said at least one actuationcell for one or more characteristics.
 14. A system for determining thecross direction responses and mappings of actuation cells extendingacross the width of a machine used for manufacturing a web of sheetmaterial as claimed in claim 13 wherein the amplitude of said perturbingsignal is gradually increased from a low level to a level at which webcharacteristic perturbations resulting from said perturbing signal aredistinguishable from noise perturbations encountered during normalmachine operation.
 15. A system for determining the cross directionresponses and mappings of actuation cells extending across the width ofa machine used for manufacturing a web of sheet material as claimed inclaim 13 wherein the duration of alternations of said perturbing signalis randomly distributed between defined limits.
 16. A system fordetermining the cross direction responses and mappings of actuationcells extending across the width of a machine used for manufacturing aweb of sheet material, the system comprising:excitation patterngenerating means for applying perturbing signals to a plurality of saidactuation cells, said perturbing signals alternating about a neutralstate of said actuation cells to minimize mean effects over any giventime period of signal application; sensor means for monitoring the webof sheet material and generating a profile signal representative of oneor more characteristics of the web of sheet material in the machinecross direction; and processor means for correlating the perturbingsignals and the profile signal to determine the cross direction responseand mapping of said plurality of actuation cells for one or morecharacteristics.
 17. A system for determining the cross directionresponses and mappings of actuation cells extending across the width ofa machine used for manufacturing a web of sheet material as claimed inclaim 16 wherein said perturbing signals comprise a plurality ofsubstantially independent excitation patterns.
 18. A system fordetermining the cross direction responses and mappings of actuationcells extending across the width of a machine used for manufacturing aweb of sheet material as claimed in claim 16 wherein said perturbingsignals comprise a plurality of statistically independent pseudo-randombinary sequences.
 19. A system for determining the cross directionresponses and mappings of actuation cells extending across the width ofa machine used for manufacturing a web of sheet material as claimed inclaim 16 wherein perturbing signals are applied to all of said actuationcells, said perturbing signals comprising a plurality of statisticallyindependent pseudo-random binary sequences.
 20. A system for determiningthe cross direction responses and mappings of actuation cells extendingacross the width of a machine used for manufacturing a web of sheetmaterial as claimed in claim 19 wherein said perturbing signals areapplied in groups of repetitively occurring statistically independentpseudo-random binary sequences, said groups being of sufficient sizesuch that recurring perturbing signals are spaced from one another by asufficient distance to preclude significant interference therebetween.21. A system for determining the cross direction responses and mappingsof actuation cells extending across the width of a machine used formanufacturing a web of sheet material, the system comprising:excitationpattern generating means for applying a perturbing signal u(k,t) to ak-th actuation cell during time t, said perturbing signal u(k,t)alternating about a neutral state of said k-th actuation cell tominimize mean effects over any given time period of signal application;sensor means for monitoring the web of sheet material and generating aprofile signal y(i,t) where i indicates the cross direction location andt indicates the time, said profile signal being representative of one ormore characteristics of the web of sheet material in the machine crossdirection and including the effects of said perturbing signal u(k,t) onsaid one or more characteristics; and processor means for correlatingsaid perturbing signal u(k,t) and said profile signal y(i,t) todetermine the cross direction response r(k,i) of the k-th actuation cellat the i-th cross direction location which also defines the mapping ofthe k-th actuation cell into the cross direction locations i for saidone or more characteristics.